/**
 * @license
 * Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 *   * Redistributions of source code must retain the above copyright notice,
 * this list of conditions and the following disclaimer.
 *   * Redistributions in binary form must reproduce the above copyright notice,
 * this list of conditions and the following disclaimer in the documentation
 * and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */

import { GLMAT_ARRAY_TYPE } from './common';

/**
 * @class 3x3 Matrix
 * @name mat3
 */

var mat3 = {};

/**
 * Creates a new identity mat3
 *
 * @returns {mat3} a new 3x3 matrix
 */
mat3.create = function() {
    var out = new GLMAT_ARRAY_TYPE(9);
    out[0] = 1;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = 1;
    out[5] = 0;
    out[6] = 0;
    out[7] = 0;
    out[8] = 1;
    return out;
};

/**
 * Copies the upper-left 3x3 values into the given mat3.
 *
 * @param {mat3} out the receiving 3x3 matrix
 * @param {mat4} a   the source 4x4 matrix
 * @returns {mat3} out
 */
mat3.fromMat4 = function(out, a) {
    out[0] = a[0];
    out[1] = a[1];
    out[2] = a[2];
    out[3] = a[4];
    out[4] = a[5];
    out[5] = a[6];
    out[6] = a[8];
    out[7] = a[9];
    out[8] = a[10];
    return out;
};

/**
 * Creates a new mat3 initialized with values from an existing matrix
 *
 * @param {mat3} a matrix to clone
 * @returns {mat3} a new 3x3 matrix
 */
mat3.clone = function(a) {
    var out = new GLMAT_ARRAY_TYPE(9);
    out[0] = a[0];
    out[1] = a[1];
    out[2] = a[2];
    out[3] = a[3];
    out[4] = a[4];
    out[5] = a[5];
    out[6] = a[6];
    out[7] = a[7];
    out[8] = a[8];
    return out;
};

/**
 * Copy the values from one mat3 to another
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
mat3.copy = function(out, a) {
    out[0] = a[0];
    out[1] = a[1];
    out[2] = a[2];
    out[3] = a[3];
    out[4] = a[4];
    out[5] = a[5];
    out[6] = a[6];
    out[7] = a[7];
    out[8] = a[8];
    return out;
};

/**
 * Set a mat3 to the identity matrix
 *
 * @param {mat3} out the receiving matrix
 * @returns {mat3} out
 */
mat3.identity = function(out) {
    out[0] = 1;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = 1;
    out[5] = 0;
    out[6] = 0;
    out[7] = 0;
    out[8] = 1;
    return out;
};

/**
 * Transpose the values of a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
mat3.transpose = function(out, a) {
    // If we are transposing ourselves we can skip a few steps but have to cache some values
    if (out === a) {
        var a01 = a[1], a02 = a[2], a12 = a[5];
        out[1] = a[3];
        out[2] = a[6];
        out[3] = a01;
        out[5] = a[7];
        out[6] = a02;
        out[7] = a12;
    } else {
        out[0] = a[0];
        out[1] = a[3];
        out[2] = a[6];
        out[3] = a[1];
        out[4] = a[4];
        out[5] = a[7];
        out[6] = a[2];
        out[7] = a[5];
        out[8] = a[8];
    }

    return out;
};

/**
 * Inverts a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
mat3.invert = function(out, a) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8],

        b01 = a22 * a11 - a12 * a21,
        b11 = -a22 * a10 + a12 * a20,
        b21 = a21 * a10 - a11 * a20,

        // Calculate the determinant
        det = a00 * b01 + a01 * b11 + a02 * b21;

    if (!det) {
        return null;
    }
    det = 1.0 / det;

    out[0] = b01 * det;
    out[1] = (-a22 * a01 + a02 * a21) * det;
    out[2] = (a12 * a01 - a02 * a11) * det;
    out[3] = b11 * det;
    out[4] = (a22 * a00 - a02 * a20) * det;
    out[5] = (-a12 * a00 + a02 * a10) * det;
    out[6] = b21 * det;
    out[7] = (-a21 * a00 + a01 * a20) * det;
    out[8] = (a11 * a00 - a01 * a10) * det;
    return out;
};

/**
 * Calculates the adjugate of a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
mat3.adjoint = function(out, a) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8];

    out[0] = (a11 * a22 - a12 * a21);
    out[1] = (a02 * a21 - a01 * a22);
    out[2] = (a01 * a12 - a02 * a11);
    out[3] = (a12 * a20 - a10 * a22);
    out[4] = (a00 * a22 - a02 * a20);
    out[5] = (a02 * a10 - a00 * a12);
    out[6] = (a10 * a21 - a11 * a20);
    out[7] = (a01 * a20 - a00 * a21);
    out[8] = (a00 * a11 - a01 * a10);
    return out;
};

/**
 * Calculates the determinant of a mat3
 *
 * @param {mat3} a the source matrix
 * @returns {Number} determinant of a
 */
mat3.determinant = function (a) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8];

    return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20);
};

/**
 * Multiplies two mat3's
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the first operand
 * @param {mat3} b the second operand
 * @returns {mat3} out
 */
mat3.multiply = function (out, a, b) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8],

        b00 = b[0], b01 = b[1], b02 = b[2],
        b10 = b[3], b11 = b[4], b12 = b[5],
        b20 = b[6], b21 = b[7], b22 = b[8];

    out[0] = b00 * a00 + b01 * a10 + b02 * a20;
    out[1] = b00 * a01 + b01 * a11 + b02 * a21;
    out[2] = b00 * a02 + b01 * a12 + b02 * a22;

    out[3] = b10 * a00 + b11 * a10 + b12 * a20;
    out[4] = b10 * a01 + b11 * a11 + b12 * a21;
    out[5] = b10 * a02 + b11 * a12 + b12 * a22;

    out[6] = b20 * a00 + b21 * a10 + b22 * a20;
    out[7] = b20 * a01 + b21 * a11 + b22 * a21;
    out[8] = b20 * a02 + b21 * a12 + b22 * a22;
    return out;
};

/**
 * Alias for {@link mat3.multiply}
 * @function
 */
mat3.mul = mat3.multiply;

/**
 * Translate a mat3 by the given vector
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to translate
 * @param {vec2} v vector to translate by
 * @returns {mat3} out
 */
mat3.translate = function(out, a, v) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8],
        x = v[0], y = v[1];

    out[0] = a00;
    out[1] = a01;
    out[2] = a02;

    out[3] = a10;
    out[4] = a11;
    out[5] = a12;

    out[6] = x * a00 + y * a10 + a20;
    out[7] = x * a01 + y * a11 + a21;
    out[8] = x * a02 + y * a12 + a22;
    return out;
};

/**
 * Rotates a mat3 by the given angle
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to rotate
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat3} out
 */
mat3.rotate = function (out, a, rad) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8],

        s = Math.sin(rad),
        c = Math.cos(rad);

    out[0] = c * a00 + s * a10;
    out[1] = c * a01 + s * a11;
    out[2] = c * a02 + s * a12;

    out[3] = c * a10 - s * a00;
    out[4] = c * a11 - s * a01;
    out[5] = c * a12 - s * a02;

    out[6] = a20;
    out[7] = a21;
    out[8] = a22;
    return out;
};

/**
 * Scales the mat3 by the dimensions in the given vec2
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to rotate
 * @param {vec2} v the vec2 to scale the matrix by
 * @returns {mat3} out
 **/
mat3.scale = function(out, a, v) {
    var x = v[0], y = v[1];

    out[0] = x * a[0];
    out[1] = x * a[1];
    out[2] = x * a[2];

    out[3] = y * a[3];
    out[4] = y * a[4];
    out[5] = y * a[5];

    out[6] = a[6];
    out[7] = a[7];
    out[8] = a[8];
    return out;
};

/**
 * Copies the values from a mat2d into a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat2d} a the matrix to copy
 * @returns {mat3} out
 **/
mat3.fromMat2d = function(out, a) {
    out[0] = a[0];
    out[1] = a[1];
    out[2] = 0;

    out[3] = a[2];
    out[4] = a[3];
    out[5] = 0;

    out[6] = a[4];
    out[7] = a[5];
    out[8] = 1;
    return out;
};

/**
* Calculates a 3x3 matrix from the given quaternion
*
* @param {mat3} out mat3 receiving operation result
* @param {quat} q Quaternion to create matrix from
*
* @returns {mat3} out
*/
mat3.fromQuat = function (out, q) {
    var x = q[0], y = q[1], z = q[2], w = q[3],
        x2 = x + x,
        y2 = y + y,
        z2 = z + z,

        xx = x * x2,
        yx = y * x2,
        yy = y * y2,
        zx = z * x2,
        zy = z * y2,
        zz = z * z2,
        wx = w * x2,
        wy = w * y2,
        wz = w * z2;

    out[0] = 1 - yy - zz;
    out[3] = yx - wz;
    out[6] = zx + wy;

    out[1] = yx + wz;
    out[4] = 1 - xx - zz;
    out[7] = zy - wx;

    out[2] = zx - wy;
    out[5] = zy + wx;
    out[8] = 1 - xx - yy;

    return out;
};

/**
* Calculates a 3x3 normal matrix (transpose inverse) from the 4x4 matrix
*
* @param {mat3} out mat3 receiving operation result
* @param {mat4} a Mat4 to derive the normal matrix from
*
* @returns {mat3} out
*/
mat3.normalFromMat4 = function (out, a) {
    var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
        a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
        a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
        a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],

        b00 = a00 * a11 - a01 * a10,
        b01 = a00 * a12 - a02 * a10,
        b02 = a00 * a13 - a03 * a10,
        b03 = a01 * a12 - a02 * a11,
        b04 = a01 * a13 - a03 * a11,
        b05 = a02 * a13 - a03 * a12,
        b06 = a20 * a31 - a21 * a30,
        b07 = a20 * a32 - a22 * a30,
        b08 = a20 * a33 - a23 * a30,
        b09 = a21 * a32 - a22 * a31,
        b10 = a21 * a33 - a23 * a31,
        b11 = a22 * a33 - a23 * a32,

        // Calculate the determinant
        det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;

    if (!det) {
        return null;
    }
    det = 1.0 / det;

    out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
    out[1] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
    out[2] = (a10 * b10 - a11 * b08 + a13 * b06) * det;

    out[3] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
    out[4] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
    out[5] = (a01 * b08 - a00 * b10 - a03 * b06) * det;

    out[6] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
    out[7] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
    out[8] = (a30 * b04 - a31 * b02 + a33 * b00) * det;

    return out;
};

/**
 * Returns Frobenius norm of a mat3
 *
 * @param {mat3} a the matrix to calculate Frobenius norm of
 * @returns {Number} Frobenius norm
 */
mat3.frob = function (a) {
    return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + Math.pow(a[6], 2) + Math.pow(a[7], 2) + Math.pow(a[8], 2)))
};


export default mat3;
